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364Anti-Realism and Anti-Revisionism in Wittgenstein’s Philosophy of MathematicsGrazer Philosophische Studien 97 (3): 451-474. 2020.Since the publication of the Remarks on the Foundations of Mathematics, Wittgenstein’s interpreters have endeavored to reconcile his general constructivist/anti-realist attitude towards mathematics with his confessed anti-revisionary philosophy. In this article, the author revisits the issue and presents a solution. The basic idea consists in exploring the fact that the so-called “non-constructive results” could be interpreted so that they do not appear non-constructive at all. The author substa…Read more
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268On Ramsey’s reason to amend Principia Mathematica’s logicism and Wittgenstein’s reactionSynthese 2020 (1): 2629-2646. 2020.In the Foundations of Mathematics, Ramsey attempted to amend Principia Mathematica’s logicism to meet serious objections raised against it. While Ramsey’s paper is well known, some questions concerning Ramsey’s motivations to write it and its reception still remain. This paper considers these questions afresh. First, an account is provided for why Ramsey decided to work on his paper instead of simply accepting Wittgenstein’s account of mathematics as presented in the Tractatus. Secondly, evidenc…Read more
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34Numbers in Elementary PropositionsNordic Wittgenstein Review 6 (1): 85-103. 2017.It is often held that Wittgenstein had to introduce numbers in elementary propositions due to problems related to the so-called colour-exclusion problem. I argue in this paper that he had other reasons for introducing them, reasons that arise from an investigation of the continuity of visual space and what Wittgenstein refers to as ‘intensional infinity’. In addition, I argue that the introduction of numbers by this route was prior to introducing them _via_ the colour-exclusion problem. To concl…Read more
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30Wittgenstein, formalism, and symbolic mathematicsKriterion: Journal of Philosophy 61 (145): 31-53. 2020.ABSTRACT In a recent essay, Sören Stenlund tries to align Wittgenstein’s approach to the foundations and nature of mathematics with the tradition of symbolic mathematics. The characterization of symbolic mathematics made by Stenlund, according to which mathematics is logically separated from its external applications, brings it closer to the formalist position. This raises naturally the question whether Wittgenstein holds a formalist position in philosophy of mathematics. The aim of this paper i…Read more
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20Haecceitism in the Tractatus: A refutation of Ishiguro’s view on Tractarian namesAnalysis 81 (2): 232-240. 2021.In a seminal essay, Hidé Ishiguro argued that names in the Tractatus are ‘like dummy names’ and that a simple object is to be conceived of as ‘an instantiation of an irreducible predicate’. In this paper, I argue that Ishiguro’s view is incompatible with other claims made in the Tractatus and should be abandoned for this reason. To this end, I adopt a two-step strategy. First, I show that Ishiguro’s view implies the adoption of an anti-haecceitistic position. Then I show that the Tractatus allow…Read more
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13Peirce’s influence on Haack's reflections on the nature of logicCognitio 22 (1). 2021.In her book Deviant Logic, Susan Haack argued for a “pragmatist” conception of logic. This conception holds that, logic is a theory on a par with other scientific theories, differing only from such theories by its degree of generality and the choice of a particular logic is to be made based on pragmatist principles, namely, economy, coherence, and simplicity. This view was contrasted, in this book, with an “absolutist” view of logic, according to which logical laws are necessary and immune to re…Read more
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7Apresentação do número pelos editores convidadosAnalytica. Revista de Filosofia 25 (2): 4-6. 2023.
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5The Number of Things in the World and the Autonomy of LogicAnalytica. Revista de Filosofia 25 (2): 125-134. 2023.Em seu livro recente, Engelmann (2021) avançou uma leitura do Tractatus que, a seu ver, removeria as dificuldades presentes em outras leituras (em particular, nas leituras “metafísica” e “resoluta”). Neste artigo, ocupar-me-ei da crítica de Engelmann às leituras metafísicas do Tractatus. Tal crítica baseia-se na ideia de que essas leituras estão comprometidas com algumas necessidades de re, o que violaria a autonomia da lógica e a ideia Tractariana segundo a qual só há necessidade lógica. Analis…Read more
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3Wittgenstein e o problema da consistência da aritméticaAnalytica. Revista de Filosofia 21 (1): 143-169. 2018.RESUMO: O objetivo deste artigo é estruturar, em torno de uma única ideia fundamental, a saber, a de que não há atalhos pela lógica, os diversos comentários de Wittgenstein à época das conversas com Waismann e o círculo de Viena sobre o problema da consistência da aritmética. Observações notórias sobre as noções de consistência, trivialidade e negação na matemática são consideradas do ponto de vista dessa sistematização. Analisa-se também em que medida esses comentários correspondem a um desenvo…Read more
Anderson Nakano
Pontifícia Universidade Católica de São Paulo
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Pontifícia Universidade Católica de São PauloProfessor